Microelectromechanical (MEM) resonators are being developed to miniaturize oscillators and filters for a number of applications including wireless communications and radio-frequency (RF) systems. MEM resonators are less bulky than the conventional quartz crystal and surface acoustic wave (SAW) oscillators which they can replace. Additionally, the MEM resonators can be fabricated using conventional semiconductor IC processes so that they can be directly integrated into an IC for reduced cost and size. Batch fabrication and the ability to place arrays of MEM resonators onto a single chip for use as filters and oscillators is also appealing for a number of high volume RF transceiver applications such as cell phones. For such applications, a frequency tolerance is required which is beyond that currently available with conventional MEM fabrication processes without post-fabrication laser trimming.
The present invention overcomes the limitations of the prior art by providing a method for designing and making MEM resonators which have a resonant frequency f0 which can be made substantially insensitive to manufacturing variations including an edge bias. This is advantageous since profitable commercial production of batch-fabricated MEM resonators and other types of MEM devices relies on attaining a high reliability and a high fabrication yield. If such devices are not designed up-front to be robust to manufacturing variations, then exhaustive post-fabrication screening, calibration, or laser trimming is often required. The MEM resonators fabricated according to the present invention, which have a reduced manufacturing variation Δf in the resonant frequency f0, are expected to significantly reduce the need for post-fabrication screening, calibration and laser trimming.
These and other advantages of the present invention will become evident to those skilled in the art.